Japanese architects have won a competition to design the first dedicated museum for the V&A outside London, a low-slung angular building on the banks of the river Tay. The "bold and ambitious" design by Kengo Kuma & Associates, a two-part structure of close-fitting slabs made from a stone compound and glass, is proposed for a site in former docks in Dundee, partly sunk into the river Tay.

It would be the V&A's first permanent outpost outside Kensington but the project's backers, a consortium including the city council and Dundee's two universities, said they face a tough fight to secure the £45m needed to finance the building.

Lesley Knox, chair of the project board, said Kengo Kuma's proposal was the most suitable of six "exciting and dynamic" designs from around the world and had won the unanimous votes of the selection committee. "What really swung it is that not only is it an incredibly exciting design, but it also works for us in Dundee. You can design buildings that can go anywhere in the world and you can design exciting buildings which are exactly right for this site," she said.

Rather than pure stone, the winning design uses a strong compound stone which can be manufactured to exact specifications and is more durable and stain-resistant than concrete, ideal for its exposed position on the Tay, Knox said. It features viewing terraces protected from the weather and an "extraordinary" central hall. The two sections would frame the research ship Discovery, used by Captain Scott to explore the Antarctic.

Competing proposals included a rock-shaped building by Vienna's Delugan Meissl Associated Architects and a large glass building by New York-based firm REX which echoed a jutting rock crystal.

Kengo Kuma has designed museums in Japan, including the Suntory museum of art and Masanari Murai art museum in Tokyo, and large corporate buildings such as the Asahi Broadcasting Corporation headquarters in Osaka.

The future of the Dundee plan hinges on whether the Scottish government will support it when the budget is fixed. The project needs £15m from the devolved government and similar amounts from European and lottery funds, and from private sector donors.

Unlike the Tate's offshoots in St Ives and Liverpool, the V&A in Dundee will not house a permanent V&A collection and the parent museum will not meet any of Dundee's costs. But it has signed a 20-year deal to send two or three travelling exhibitions there each year.

The V&A has been staging temporary exhibitions in Sheffield for 10 years and is in protracted talks to have a similar 10-year deal with Blackpool. Dundee's supporters, including the city's Labour and Scottish National party MPs, believe it would help drive the city's economic regeneration.

Knox confirmed it was still far from clear whether the money would be available given the heavy public spending cuts. "Everybody has we've made compelling case, but it's tough times and therefore until the decision is made, we can't prejudge that," she said. "All I can say is we've worked our tails off to make sure we've made our case, and the feedback has been positive."